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I'm quite new to physics so this question may sound dumb for many of you. But when I was learning about uniform circular motion, all sources I can find talks about centripetal acceleration, and, when multiplied by mass, the centripetal force. However, when I tried to look up centripetal velocity, I found nothing.

According to my understanding, if there's an acceleration and it's not balanced out(which it's not, because it can actually change the direction of the tangential velocity) then it must induce a velocity. If so, why doesn't the body get closer and closer toward the centre of the circle?

In projectile motion, we know that X and Y motions are unrelated and do not affect each other, could this also be the case in circular motion? The tangential velocity and the centripetal velocity(if exists) are perpendicular and therefore do not affect each other, but together they affect to direction of the body's motion. It's just that in projectile motion, the Y motion always points to the ground, causing a parabolic motion, whereas in circular motion the centripetal acceleration always changes direction(always points to the centre of circle) which is why a circular path is caused. Am I right?

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    $\begingroup$ It is useful to know the etymology of centripetal. Centrum is center and petere is seeking. And if you're traveling a circle, you aren't heading toward (seeking) the center. However, as @Guy said, there's a turning force which heads into (seeks) the center of the circle $\endgroup$ Jun 12 '20 at 21:14
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Centripetal force always points radially inwards. But the object is always moving tangentially. Thus, the force vector is acting at right angles to the velocity vector. In this situation, there is no force acting in the direction of its velocity so its speed does not increase. Instead it accelerates sideways. This causes all the vectors to rotate.

Circular motion is a condition of constant radial acceleration. If there were such a thing as centripetal velocity it would accumulate over time and approach infinity. Fortunately, there is no such thing and speed remains constant.

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  • $\begingroup$ This doesn't disprove the existence of a centripetal velocity being balanced out by a centrifugal velocity, perpendicular to the tangent and always pointing away from the center, alongside a centrifugal acceleration which is unbalanced by a much larger centripetal acceleration. This'd allow for the existence of centripetal acceleration and force, but centripetal velocity and momentum would always be equal to zero. $\endgroup$
    – DonielF
    Jul 28 '20 at 0:30
  • $\begingroup$ @DonielF You cannot disprove the existence of anything, not even of the Flying Spaghetti Monster. Discussing hypothetical opposites is metaphysics, not physics. $\endgroup$ Jul 28 '20 at 7:54
  • $\begingroup$ There is no obvious reason why centripetal velocity "would accumulate over time and approach infinity". But if there was non-zero centripetal velocity, the distance of the particle from the center would be changing, and that is not uniform circular motion. $\endgroup$
    – alephzero
    Oct 15 '20 at 1:14

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